Frictional Pressure Gradient Research Articles

Numerical modeling of laminar and turbulent annular flows of power-law fluids in partially blocked geometries

The presence of cuttings bed in deviated wellbores has an undesirable effect on wellbore hydraulics by reducing the open flow area. In addition, pipe eccentricity affects the annular frictional pressure gradient under such configurations. The lack of practical correlations to account for the combined effects of cuttings bed and eccentricity on frictional pressure gradient of power-law fluids is the major motivation of this study. Thus, the effect of partially blocked eccentric annuli on frictional pressure gradient of power-law fluids is investigated. A numerical model is first developed to realize the laminar and turbulent annular flow of power-law fluids in eccentric configurations. The numerical solution of the governing equations is pursued using the finite difference method. The results of our numerical model are verified through comparisons with the published results of frictional pressure gradients in the literature. The numerical results indicate that with an increase in cuttings bed height the frictional pressure gradient can increase exponentially. Numerous simulation scenarios are considered for the flow of power-law fluids in partially blocked eccentric annuli. Then, the simulation results are fitted using regression analysis to obtain explicit correlations for the prediction of laminar and turbulent frictional pressure losses. The proposed correlations are essential for an accurate estimation of the annular frictional pressure gradient and equivalent circulating density, which ensures safe and optimized drilling operations.

Flow Boiling of R450A, R515B, and R1234ze(E) Inside a 7.0 mm OD Microfin Tube: Experimental Comparison and Analysis of Boiling Mechanisms

A comparative analysis of the flow boiling characteristics of R450A, R515B, and R1234ze(E) inside a 7.0 mm OD microfin tube was performed. The mass velocity was explored from low values, starting from 50 kg m−2 s−1, up to 400 kg m−2 s−1, and the heat flux was tested in the range of 10–50 kW m−2, keeping a constant saturation temperature of 30 °C at the inlet of the test section. R515B and R1234ze(E) showed similar values of the heat transfer coefficient and frictional pressure gradient under all the investigated working conditions. R450A showed lower values of the heat transfer coefficient, especially at low heat flux and high mass velocity, compared to R515B and R1234ze(E), but the gap of the heat transfer performance between the three fluids reduced at high heat flux. The frictional pressure drops of R450A were generally lower than those of R515B and R1234ze(E). In the end, some correlations for the evaluation of both the heat transfer coefficient and the pressure drop were selected, and the estimated values were compared against the experimental counterpart. Furthermore, the effects of nucleate boiling and of convective boiling, as well as of the temperature glide for R450A, were analyzed and estimated.

Frictional Pressure Drop for Gas–Liquid Two-Phase Flow in Coiled Tubing

Coiled tubing (CT) is widely used in drilling, workover, completion, fracturing and stimulation in the field of oil and gas exploration and development. During CT operation, the tubing will present a gas–liquid two-phase flow state. The prediction of frictional pressure drop for fluid in the tube is an important part of hydraulic design, and its accuracy directly affects the success of the CT technique. In this study, we analyzed the effects of the gas void fraction, curvature ratio and fluid inlet velocity on frictional pressure drop in CT, numerically. Experimental data verified simulated results. Flow friction sensitivity analysis shows the frictional pressure drop reaches its peak at a gas void fraction of 0.8. The frictional pressure gradient increases with the increase in curvature ratio. As the strength of secondary flow increases with the increase in inlet velocity, the increased trend of gas–liquid two-phase flow friction is aggravated. The correlation of friction factor for gas–liquid two-phase flow in coiled tubing is developed by regression analysis of simulation results. The research results can support high quality CT hydraulics design, through which the success of CT operations can be guaranteed.

A New Two-Phase Multiplier for Flow Pressure Drop in Multiport Minichannel Condensers and Evaporators

Due to flow maldistribution, the condensation and evaporation flow patterns in multiport minichannels are considerably different from single minichannels or macrochannels. This article compiled the friction pressure drop data from experimental phase-change investigations in multiport minichannel condensers and evaporators over the past two decades. The data was reduced to friction pressure gradients, and a new two-phase multiplier was proposed for estimating the phase-change pressure drop in multiport condensers and evaporators. Thirteen hundred and forty-four condensation pressure drop and six hundred and twenty-three evaporation pressure drop data from twenty-nine studies were correlated to yield four predictive two-phase multiplier equations in the laminar and turbulent flow regimes. The predictive correlations fit 67% of the laminar condensation and 80% of the turbulent pressure drop data within ±50%. Further, 57% of the laminar evaporation and 100% of the turbulent evaporation pressure drop data were fit within ±50%. The correlations were compared with widely published correlations and were a significant improvement. Meta-analysis revealed that multiport minichannels are most effective for reducing turbulent flow condensation pressure drop and laminar flow evaporation pressure drop. The compiled data and presented correlations and analysis should be helpful to the process, electronics packaging, aviation, and aerospace industries designing compact, lightweight, and high-efficiency condensers, and evaporators.

CFD Simulation of the Hydrodynamics of Core-Annular Flow of Oil, Gas and Water in Elliptic-Cylindrical Duct

Heavy oils, due to their high viscosity, have greater viscous resistance to flow, requiring high pumping power for transport and increasing operating cost. As an alternative to minimize this problem, the core-flow technique emerged, which consists of injecting water simultaneously with the oil flow, causing the heavy oil to be surrounded by a layer of water and flowing in the center of the duct without touching the pipe wall, consequently reducing the friction pressure gradient. Thus, this work aims to numerically study the core-annular flow of oil, water and gas in a cylindrical duct with an elliptical cross-section, considering a three-dimensional, isothermal and incompressible flow. For the numerical solution of the governing equations, the software Ansys FLUENT 15.0 was used. It was found that the lubrication provided by the water on the duct wall reduced the pressure variation by 7.20 times compared to the heavy oil single-phase flow, proving the good efficiency of the core-flow technique.

Experimental investigation on the flow condensation of R450A, R515B, and R1234ze(E) in a 7.0 mm OD micro-fin tube

The flow condensation of R1234ze(E), R450A, and R515B was conducted in a 6.14 mm inner diameter micro-fin tube. The fin height is 0.18 mm and the fin number is 50. The helix angle is 18° and the area enhancement factor is 1.63. During the experimental tests, the saturation temperature is 30 and 40 °C. The mass fluxes range from 50 to 400 kg m-2 s-1. The vapor qualities are between 0.1 and 0.96. The heat transfer coefficients and frictional pressure gradients of the three refrigerants were compared with each other. The experimental heat transfer coefficient increases with vapor quality and mass velocity, except at high vapor quality, where a higher mass velocity does not imply a higher heat transfer coefficient, probably due to the liquid film thickness distribution. Generally speaking, R450A presents slightly higher heat transfer coefficients at high mass fluxes and smaller pressure gradients, whereas R515B shows lower heat transfer coefficients and pressure drops very close to those of R1234ze(E). Moreover, some models of the heat transfer coefficient and pressure gradient specifically developed for micro-fin tubes were chosen to explore their feasibility for the new refrigerants and tube. Cavallini et al.’s model shows the best agreement for the heat transfer coefficient, and Diani et al.’s model shows the best agreement for the frictional pressure gradient.

A multispecies 1D concentration distribution model for coarse‐particle slurries

AbstractCoarse‐particle (settling) slurry pipelines are key process units in many industries. In Canada's oil sands operations, such pipelines represent hundreds of millions of dollars of infrastructure investment and transport thousands of tonnes of solids every hour. The ability to determine key design/operating parameters of a settling slurry, such as frictional pressure gradient and deposition velocity, is dependent on the accuracy of the concentration distribution model used to determine the local concentration of coarse solids as a function of vertical position within the pipe. Accurate predictions of the concentration profile are also required for physics‐based models of particle‐impact erosion in slurry pipelines. In this study, an improved concentration distribution model was developed. The classic Schmidt‐Rouse turbulent diffusion equation forms the basis for the model. The improvements made here include the use of a more suitable, high‐concentration hindered settling velocity correlation, and a simple semi‐empirical correlation for the particle diffusivity, which is shown to be dependent only upon the terminal particle settling velocity and the Kolmogorov turbulent velocity scale. The model is applicable to slurries with broad size distributions and/or species with different densities. The performance of the model is tested against numerous slurry flow conditions, including particles from 70 μm to 8 mm in diameter, pipe diameters of 76 mm ≤ D ≤ 500 mm, and in situ solids volume concentrations from 0.10 to 0.45. The concentration distribution predictions are shown to be in excellent agreement with the measurements.

Pressure-drop characteristics of CO2 boiling flow in the regenerative-cooling channel of an Mg/CO2 powder rocket engine for Mars missions

To solve the problem of the thermal protection of Mg/CO2 powder rocket engines, how different working conditions in the regenerative-cooling channel influence the pressure drop of CO2 coolant is investigated. It is found that the proportion of two-phase acceleration pressure drop increases with increasing CO2 mass flux, inlet temperature, and heat flux and decreases with increasing backpressure. The ratio of acceleration pressure drop to total pressure drop is ∼0.3. With increasing mass flux, incoming flow temperature, and heat flux, the two-phase frictional pressure drop increases, and the increase of backpressure decreases the two-phase frictional pressure gradient. The factor flp is introduced to correct for the local pressure drop of the experimental system, and flp = 1.9819 when the two-phase coolant Reynolds number is between 20 000 and 50 000. For the unidirectionally heated cooling channel, the coolant is heated unevenly therein, so the heat-transfer mode has an important influence on the frictional pressure gradient of the coolant. It is found that μl can be used to predict the frictional pressure drop of μtp, but the deviation is still more than 20%. Based on experimental data, a new correlation for predicting the two-phase frictional pressure gradient is proposed. The relative deviation of the predicted data is only −7.02%, and 96.12% of the predicted data fall within the ±15% deviation band, so the prediction accuracy is greatly improved. The present research provides a theoretical basis for designing a regenerative-cooling scheme for an Mg/CO2 powder rocket engine.

Machine-learning-based heat transfer and pressure drop model for internal flow condensation of binary mixtures

Machine learning regression models were developed to predict the heat transfer coefficient and frictional pressure gradient during condensation of three zeotropic mixtures (ethane/propane, R245fa/pentane, and R410A) in micro- and macro-channels (0.76 mm < D < 14.45 mm). 1032 data points were used to train, test, and validate four machine learning models: support vector regression (SVR), random forest regression (RFR), gradient boost (GB), and artificial neural networks (ANN). For data not used for training, SVR predicted the apparent Nusselt number the best, with a mean absolute percent error (MAPE) of 5.0%, while GB predicted the two-phase friction factor the best with a MAPE of 5.5%. To determine the impact of the additional heat and mass transfer resistances in zeotropic condensation, Shapley analysis was performed on the models to weigh the importance of all dimensionless parameters used to predict the heat transfer and pressure drop. Overall, the three most important parameters to predict heat transfer were the Reynolds number of both phases and a dimensionless temperature glide; while the most important parameters to predict pressure drop were the Bond number, Weber number, and vapor-phase Reynolds number. The importance of mass transfer is discussed along with the applicability of other simple mixture models.

Effect of salt and particles on the hydrodynamics of foam flows in relation to foam static characteristics

• Investigated the effect of salt and particles on dynamic behaviour of foam flow. • Characterised regimes of three-phase foam flow using signal analysis of pressure data. • Demonstrated the effect of salt and particle on the frictional pressure of foam flow. Foam flows containing particles are present in many applications including mining, wastewater treatment, environmental remediation of contaminants such as PFAS using foam fractionation, dewatering of gas wells and particle cleanout in pipelines. These applications usually involve dissolved salts and solid particulates, which may have a positive or adverse impact on the foam flow and its performance depending on the application, the system’s constituents (e.g., type and concentration of salt/particles) and the operating condition (e.g., gas and liquid flowrates). This work aims to investigate the effect of salts (primarily NaCl) up to 0.2 M salt and solid particulates (mainly clay) up to 25 g/L particles on the dynamic behaviour of 200 ppm sodium dodecylbenzene sulfonate (SDBS) foam flows, frictional and hydrostatic pressure gradient, foam holdup and flow regimes in a vertical column. Flow regimes are analysed through power spectral density (PSD) and the probability density function of differential pressure data. The results show that salt and particles affect the foaming performance of SDBS solutions, thus influencing the transition of flow regimes. Our static tests show a 1.2-to-2.2-fold increase in the effect of salts and particles on the foamability of the SDBS solutions, whereas the foam flow dynamic data show a strong dependence on the hydrodynamics of the system. For example, the pressure gradient of the foam flow experienced a 16% reduction with the addition of salt and particles at low gas superficial velocity ( V sg of 0.48–2.4 m/s and fixed V sl of 0.02 m/s) due to the domination of gravitational dP/dz while it increased up to 22% at high V sg of up to 11.2 m/s due to the domination of frictional forces. Our results demonstrate that the foam static properties such as foamability, foam stability and wetness are useful to understand the stabilising mechanisms of foams. However, they cannot represent and explain the foam behaviour in dynamic systems.

Liquid Loading in Natural Gas Vertical Wells: A Review and Experimental Study

Summary Liquid loading in natural gas wells is one of the main causes of decline and eventual cease of production. Identifying the onset of liquid loading and its impacts on production is vital in production optimization of gas wells. In this study, a new state-of-the-art experimental facility is used to analyze two-phase flow parameters, such as liquid and gas velocities, pressure drop, liquid holdup, and flow pattern, and study the onset of liquid loading. Experiments are conducted using air and water in a 0.0508-m (2-in.) internal diameter (ID) vertical flow loop. The facility is designed to eliminate any source of disruption to the flow in a temperature-controlled indoor environment to avoid changes in fluid properties. A wide range of data are collected related to the onset of liquid loading and in the churn region. The acquired data are compared with other studies to ensure the accuracy and repeatability of the tests. A quantitative method is developed to predict the onset of liquid loading, namely, the positive frictional pressure gradient (negative pressure drop). A comparison is made between the visual observations for flow pattern transition, positive frictional pressure gradient, and minimum pressure drop. Overall, the results show that the positive frictional pressure gradient approach can provide a better estimation of the onset of liquid loading than the minimum pressure drop approach. Additionally, Tulsa University Fluid Flow Project (TUFFP) unified model (v2016) and OLGA (v2016.2.1) are used to evaluate the average pressure drop, liquid holdup, and flow pattern. Furthermore, the liquid film reversal model, liquid droplet models, and inflection point approach are included in the comparison of the onset of liquid loading with experimental data. The OLGA model predicts the results more precisely than other models. The comparison with the experimental data indicates that inaccurate flow pattern predictions could significantly increase the relative errors in pressure drop and liquid holdup. In addition, the evaluation of OLGA results suggests the need to develop a model for churn flow, as the relative error increases sharply in the churn flow with the model predicting the transition to slug flow.

Effect of Liquid Properties on Frictional Pressure Drop in a Gas-Liquid Two-Phase Microchannel

The flow characteristics in a ring-shaped microchannel with an inner diameter of 1 mm were studied in two-phase flow systems with air-water, air-glycerol aqueous solution and air-ethanol aqueous solution using the differential pressure method. The effects of liquid properties (surface tension and viscosity) and gas/liquid superficial velocity on frictional pressure drop were discussed. The experimental results show that the frictional pressure gradient increases with the increase of superficial gas velocity, superficial liquid velocity and liquid viscosity, and increases with the decrease of liquid surface tension, which has a good agreement with the literature values. The friction pressure drop data are compared with the classical models and correlations in literature, and a reliable correlation is proposed for prediction of two-phase friction coefficient in microchannels.

The combined effect of fluid rheology, inner pipe rotation and eccentricity on the flow of Newtonian and non-Newtonian fluid through the annuli

The accurate prediction of the fluid dynamics and hydraulics of the axial or helical flow of non-Newtonian drilling fluids in the annuli is essential for the determination and effective management of wellbore pressure during drilling operations. Previous studies have shown that the pressure losses and fluid velocity distributions in the annuli are highly influenced by the rheological properties of the fluid, inner pipe rotary speed and eccentricity. However, many studies in literature have developed or applied theoretical models that were either only valid for Newtonian annuli flows or have not considered the combined effect of the fluid rheological parameters with the inner pipe rotary speed and eccentricity when calculating the frictional annuli pressure losses for non-Newtonian shear thinning fluids. Furthermore, there have been inconsistencies in the description of the effect of inner pipe rotation on the pressure losses experienced for both Newtonian and non-Newtonian flows in concentric and eccentric annuli. In this study, an analytical and numerical approach were carried out to investigate and evaluate the hydrodynamic behaviour of the axial and helical isothermal flow of Newtonian and non-Newtonian fluids through the annuli. Techniques of computational fluid dynamics for fully developed steady-state fluid flow were applied to obtain detailed information of the flow field in the annuli. New analytical and numerical models were developed to obtain the fluid velocity and viscosity field distribution and determine the frictional pressure gradient for laminar and turbulent flows in the concentric and eccentric annuli with and without inner pipe rotation and were compared and validated favourably with models previously presented in literature. Results showed that for a fully developed flow of non-Newtonian shear thinning fluids, if the fluid flowrate is kept constant, an increase in inner pipe rotation leads to a decrease in the axial frictional pressure gradient when the pipe is rotating on its axis. For annuli flows of non-Newtonian fluids, the effect of inner pipe rotation on the axial pressure gradient is dependent on the fluid flowrate and at high fluid flowrates, the influence of the inner pipe rotation on the fluid hydraulics decreases. In general, for shear thinning non-Newtonian fluids, pipe rotation can improve the fluid flow in the region of lower flow in the eccentric annuli. Unlike the flow of Newtonian fluids through the annuli, the friction geometry parameter and thus the friction factor is highly influenced by the rheological parameters of the fluid, the fluid flowrate, inner pipe rotary speed and eccentricity.

Adiabatic frictional pressure gradient during flow boiling of pure refrigerant R1233zd and non-azeotropic mixtures R448A, R452A and R455A

The research on two-phase flow characteristics of refrigerants is of primary importance in several fields, such as air conditioning and refrigeration systems. Therefore, the determination of the pressure drop during flow boiling is important for the correct design of evaporators and heat spreaders systems. This paper presents a collection of experiments on flow boiling pressure drop using pure refrigerant R1233zd and new low-GWP refrigerant mixtures R448A, R452A and R455A. All tests were performed in adiabatic conditions, in a smooth horizontal stainless-steel tube having an internal diameter of 6.0 mm and a thickness of 1.0 mm. The effect of operating parameters, such as (bubble) saturation temperature (from 25 to 65 °C) and mass flux (from 150 to 600 kg/m2s) is investigated and discussed, and the performance of the chosen fluids is also compared. Finally, an assessment of existing prediction methods is carried-out to find the most suitable correlations for two-phase pressure drop evaluation.

Investigation on the interphase drag and wall friction in vertically oriented upward and downward two-phase flows under accident conditions in light water reactors

In this study, applicability of the one-dimensional two-fluid model for predicting the vapor void fraction and the frictional pressure drop in the adiabatic upward and downward two-phase flows has been studied through comparing model predictions with experimental data of Tikhonenko (1973) taken in the 33 mm diameter pipe at system pressure ranging from 2 to 9 MPa, and rated velocity of 0.2 to 2 m/s (mass flux of 170 to 1400 kg⋅m−2 s−1). The experiments reproduce the conditions of the two-phase coolant flow which are expected to occur in the light-water-reactor systems under loss-of-coolant accidents and design extension conditions. It has been found that the existing empirical models for interfacial and wall friction used in the current thermal–hydraulic simulation codes allow adequate prediction of the vapor void fraction and the frictional pressure drop in vertical pipes only for the upward direction of two phase flow. Modeling deficiencies have been identified when these models are applied to the low velocity downward flow. For the downward two-phase flow at a rated velocity of 0.2 m/s (mass flux of 170 kg⋅m−2 s−1), the Lockhart-Martinelli model underpredicts the frictional pressure gradient of the liquid phase which leads to the over-prediction of the average velocity of the liquid phase. As a result, the calculated void fraction is higher compared to the experiment. The possible ways to improve the current models of the wall friction in two-phase flows have been discussed.

Heat transfer coefficient, pressure drop and dry-out vapor quality of R454C. Flow boiling experiments and assessment of methods

Flow boiling heat transfer, pressure drop and dry-out vapor quality of low-GWP non-azeotropic mixture R454C are experimentally evaluated. All tests are carried out in a smooth, horizontal, stainless-steel tube having an internal diameter of 6.0 mm, heated by DC current by means of Joule effect. The influence of the operating parameters in terms of mass flux, heat flux and saturation pressure is investigated and discussed. Both mass velocity and heat flux have a positive effect on the flow boiling heat transfer coefficient, whereas the saturation pressure negatively affect the boiling performance. Frictional pressure gradients are instead seen to increase with increasing mass velocity and reducing saturation pressure, while the onset of dry-out is anticipated for higher heat and mass fluxes and is unaffected by the variation of the bubble temperature. The assessment of predictive methods is carried-out for experimental data not belonging to stratified flow and post-dry-out heat transfer, that could not be predicted by conventional flow pattern maps. Finally, some tested flow boiling heat transfer coefficient correlations provide better results when modifying their nucleate boiling contribution by taking into account the negative effect of the temperature glide during evaporation.

Effect of Tube Expansion on Heat Transfer and Pressure Drop Characteristics During Condensation in Micro-Fin Tubes

Despite of the large number of research dedicated to condensation heat transfer and pressure drop characteristics in pristine micro-fin tubes, experimental investigation on effects of tube expansion have not been reported in the open literature. The paper reports measured cross-sectional dimensions, condensation heat transfer and pressure drop data of R1234ze(E) in pristine (5.10 mm OD) and expanded (5.26 mm OD) micro-fin tubes with mass fluxes from 100 to 300 kg/(m2·s). Effects of mass flux, vapor quality and tube expansion on the heat transfer coefficients and friction pressure gradients were investigated in the study. When the mass flux is 100 kg/(m2·s), the heat transfer coefficient and pressure drop of R1234ze(E) decrease after tube expansion. However, when the mass fluxes are 200 and 300 kg/(m2·s), tube expansion effects on the heat transfer coefficient and pressure drop are not notable. In addition, the experimental results are analyzed based on the existing condensation heat transfer and pressure drop correlations.

Experimental investigation of flow and pressure drop characteristics of air-oil slug flow in a horizontal tube

This study examines two-phase flow and pressure drop characteristics associated with slug flow in a tube with an inner diameter of 4 cm. Experiments are conducted using air and low viscosity mineral oil as working fluids at atmospheric pressure and two different oil temperatures, 25 and 45°C. The superficial gas and liquid velocities are in the range of 0.33–2.43 m/s and 0.20–1.20 m/s, respectively. Flow visualization images and temporal records of pressure drop oscillation are presented for different gas and liquid superficial velocities. The relevant flow parameters associated with slug flow, such as the elongated bubble velocity, elongated bubble length, liquid slug length, and liquid film thickness, are measured, and the relationship between the slug flow parameters and the superficial gas and liquid velocities is investigated. The measured pressure gradient data are also compared to predictions of previous homogeneous equilibrium models and semi-empirical correlations for two-phase frictional pressure gradient. A theoretical slug flow model for predicting the total pressure gradient of slug unit is presented using empirical correlations for the slug flow parameters. The new model accurately predicts the experimental pressure gradient data, evidenced by an overall mean absolute error of 19.3%.

An empirical investigation on flow pattern, heat transfer, and pressure drop during flow boiling of R1234yf in an inclined plain tube

In the present study, the flow pattern, boiling heat transfer, and pressure drop of R1234yf are experimentally studied inside a plain tube with an inner diameter of 8.3 mm, the outer diameter of 9.52 mm, and the length of 670 mm, in seven different inclination angles from −90° (downward vertical flow) to +90° (upward vertical flow). The experiments are conducted at four mass velocities of 80, 160, 240, and 320 kg m−2 s−1, mean vapor quality range of 0.1–0.77, saturation temperature of 31 °C, and four heat fluxes of 4.5, 9.0, 13.5, and 18.0 kW m−2. The effects of different parameters on the heat transfer coefficient and frictional pressure drop have been investigated. Based on the results, the tube inclination angle has a significant effect on the flow patterns and heat transfer coefficient, which is more prominent at low vapor qualities and low mass velocities. For all mass velocities, the highest and lowest heat transfer coefficients are attained in the tubes with inclination angles of +90° (vertical upward flow) and −90° (vertical downward flow), respectively. The frictional pressure drop is considerably affected by the tube inclination angle, and the effect is more noticeable at high vapor qualities. At low vapor quality regions, the heat flux strongly affects the heat transfer coefficient while it has a negligible effect on the frictional pressure drop. Finally, the experimental results are compared to the existing correlations, and modified correlations are proposed to predict the heat transfer coefficient and the frictional pressure gradient of R1234yf during flow boiling inside an inclined plain tube.

A local eddy viscosity parameterization for wind-driven estuarine exchange flow. Part I: Stratification dependence

A new parameterization for the estuarine turbulent eddy viscosity coefficient is developed considering the influence of wind forcing and feedback between stratification and shear. The emerging tidally averaged eddy viscosity profile AvT is parameterized as parabolic under well-mixed conditions, and is composed of a skewed-Gaussian-like form for the upper layer, and a parabolic form for the bottom layer under stratified conditions. The precise shape of the profiles depends parametrically on the bottom boundary layer thickness, the bulk Richardson number, and the Wedderburn number. The parameterized AvT profiles show excellent agreement with profiles obtained from numerical models. To explore the importance of vertically varying AvT with regard to exchange processes, an analytical model is designed. This one-dimensional model is based on a balance between frictional forces and pressure gradient. The resulting exchange flow is analyzed over the relevant parameter space that is associated with horizontal and vertical stratification through the bulk Richardson number, and the bi-directional wind stress via the Wedderburn number. Down-estuary wind enhances the up-estuary flow near the bottom and down-estuary flow near the surface driving an exchange flow pattern typically associated with gravitational circulation. Up-estuary wind results in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow that is up-estuarine at the surface with classical two-layer circulation underneath. Three-layer flow emerges with a weak wind. With increasing runoff velocity, three-layer flow transitions to a single layer flow under weak stratification conditions.